16z^6-576z^4=0

Solution for 16z^6-576z^4=0 equation:

Simplifying
16z6 + -576z4 = 0

Reorder the terms:
-576z4 + 16z6 = 0

Solving
-576z4 + 16z6 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '16z4'.
16z4(-36 + z2) = 0

Factor a difference between two squares.
16z4((6 + z)(-6 + z)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Subproblem 3
Set the factor '(-6 + z)' equal to zero and attempt to solve:

Simplifying
-6 + z = 0

Solving
-6 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + z = 0 + 6
z = 0 + 6

Combine like terms: 0 + 6 = 6
z = 6

Simplifying
z = 6
Solution
z = {-6, 6}